1. Field of the Invention
The present embodiment of the invention relates to a geometric craft and educational kit for use in connection with craft kits. The geometric craft and educational kit has particular utility in connection with craft and educational kit based on a geometric representation of the movement of a chessboard knight.
2. Description of the Prior Art
Geometric craft and educational kits are desirable for assisting geometry educators with teaching the theoretical concepts specific to the direct moves which a knight makes on a chessboard during a closed knight tour. In this context a direct move is the resulting straight line move that would be angular in respect to the chessboard grid, versus the L shaped pattern that results from moving a knight one chessboard square at a time. A closed knight tour refers to the series of moves the knight moves when the knight begins and ends at the same chessboard square. The focus of this invention are simple four move, close knight tours which create three basic polygon shapes, a narrow rhombic, a wide rhombic and a square. These polygons can be tiled to create two and three dimensional shapes and when divided by perimeter lines represent four of the five platonic solids, hexahedron, octahedron, dodecahedron and icosahedron. The modeling set would include precut knight tour polygons for assembly into two and three dimensional shapes.
The use of craft kits is known in the prior art. For example, U.S. Pat. No. 4,310,994 to Gephardt discloses a complementary geometric construction modules, each derived from a rectangular prism, with end faces formed obliquely to each other and to the longitudinal axis of the prism, with the two oblique faces touching each other at a point on the longitudinal edge of the prism. Each module forms a hexahedron, each being the reverse or mirror-shape of the other, and providing bilateral symmetry when the two corresponding faces on the modules, are in full contact with each other. The modules in multiple sets are adapted to be formed into a wide variety of sculptured architectural shapes, unique in appearance. However, the Gephardt '994 patent does not have parts cut to represent knight tour polygons.
Similarly, U.S. Pat. No. 4,682,450 to Diamond discloses a combinate polyhedral model and in particular to a model which can be readily of use in architectural or engineering applications. A new type of complex concave polyhedron is disclosed which is formed from six-sided polyhedron units. However, the Diamond '450 patent does not have parts cut to represent knight tour polygons.
Lastly, U.S. Pat. No. 5,155,951 to Lalvani discloses a building system composed of space-filling saddle zonohedra which fit together periodically and non-periodically into a variety of orderly and irregular looking space structures. The saddle zonohedra are composed of convex or non-convex saddle polygons and are derived from the infinite class of plane-faced zonohedra. The surfaces of the saddle polygons could be continuously curved surfaces or faceted polygonal surfaces derived from minimal surfaces. The curved surfaces could be flexible membranes or nets in tension used by themselves or in combination with space frames, or stiff shell-like surfaces, and the edges of the space frames could be hinged or fixed to others. Applications of the system include architectural and environmental structures, fixed or retractable space frames, decks or platforms, educational kits or toys, curved tiles, and saddle polyhedral nodes for space frames. The building system could be used in extra-terrestrial environments where saddle-shaped “floors”, surfaces and enclosures provide interesting possibilities. However, the Lalvani '951 patent does not have parts cut to represent knight tour polygons.
While the above-described devices fulfill their respective, particular objectives and requirements, the aforementioned patents do not describe a geometric craft and educational kit that allows craft and educational kit based on a geometric representation of the movement of a chessboard knight. The Gephardt '994, Diamond '450 and Lalvani '951 patents make no provision parts cut to represent knight tour polygons.
Therefore, a need exists for a new and improved geometric craft and educational kit which can be used for craft and educational kit based on a geometric representation of the movement of a chessboard knight. In this regard, the present embodiment of the invention substantially fulfills this need.
In this respect, the geometric craft and educational kit according to the present embodiment of the invention substantially departs from the conventional concepts and designs of the prior art, and in doing so provides an apparatus primarily developed for the purpose of craft and educational kit based on a geometric representation of the movement of a chessboard knight.